It is known to produce radial-symmetrical coagulation necrosis in biological tissue with the laser radiation emanating from an optical light-wave conductor. For example, the radiation of an Nd:YAG-laser at 1.064 nm can be used with an optical fiber made of quartz glass (PCS-type, HCS-type or ALL-SILICA-type) as the radiation guiding system. For this purpose, the light-guiding fiber is either held on the tissue or inserted therein. The light distribution in the tissue takes place utilizing the inherent scattering of the particular tissue. However, the disadvantage must be accepted that a high energy density occurs at the contact location between the end surface of the fiber and the tissue. This energy density is dependent .upon the fiber diameter and leads to the carbonization of the tissue surface at a light energy above a few 100 mW and in this way, prevents a further spread of the radiation in the tissue because of the high absorption of the carbon. It is therefore necessary to realize an all-around radiation characteristic of the laser radiation at the distal end of the light conductor. For this purpose, the laser radiation exiting with limited aperture angle from the fiber must be influenced in its exiting and radiation characteristic. Accordingly, it is known to use multimode light-wave conductors for transmitting optical modes of high order (ring modes), for example, by oblique coupling in. When using a PCS-fiber, a radially symmetrical conical radiation of the laser energy is obtained after removal of the optical cladding at the distal end. At the same time, the unobstructed optical surface is protected by means of a glass tube which is attached with adhesive to the cladding on the non-decladded portion of the optical fiber. An applicator device of this kind is a commercially available product of the MBB-Medizintechnik Company with the product being known commercially as an "ITT-PROBE". Such an applicator according to the state of the art however has several disadvantages. Accordingly, the risk is present that the protective glass tube, which is only attached with adhesive, separates at the distal end and that thereby disadvantages result for the patient. On the other hand, a defined excitation of the ring mode requires an increased optical complexity at the coupling-in end.